Here's a video from Mazda.ca showing the BSM and how it works.
This is what I'd do. First, I'd head down to the dealership and advise them of the issues I'm having with the BSM on the right side. It could possibly be a faulty radar sensor, and they may be willing to swap it out. If they're not interested in helping me out, I'd borrow a friend's car (and the friend) and take both cars to an empty parking lot. I'd park my car, then measure 24-25 ft from the rear of my car and park the borrowed car there, in the space where it would be in the next lane over and in my blind spot. Then, I'd sit in my car and shoulder check to get an idea of how far the borrowed car is from my point of view, then get on a main road and attempt to recreate that distance with the borrowed car following me (or any other car). If the BSM still won't trigger after confirming that vehicles are following closely enough to trigger it, I'd take it back to the dealer and report my findings. If they were still unwilling to assist, I'd escalate accordingly (as described in the owner's manual). It would help a lot if there was recorded video of the "experiment" so there's something to show them in conjunction with Mazda.ca's video of the BSM in action.